WIAS Preprint No. 2618, (2019)

Pathwise McKean--Vlasov theory with additive noise


  • Coghi, Michele
    ORCID: 0000-0002-4198-0856
  • Deuschel, Jean-Dominique
  • Friz, Peter
    ORCID: 0000-0003-2571-8388
  • Maurelli, Mario
    ORCID: 0000-0002-3028-1742

2010 Mathematics Subject Classification

  • 60F99 60F10 60G09


  • McKean-Vlasov, interacting particles, lithium-ion batteries, large deviations




We take a pathwise approach to classical McKean-Vlasov stochastic differential equations with additive noise, as e.g. exposed in Sznitmann [34]. Our study was prompted by some concrete problems in battery modelling [19], and also by recent progress on rough-pathwise McKean-Vlasov theory, notably Cass--Lyons [9], and then Bailleul, Catellier and Delarue [4]. Such a ``pathwise McKean-Vlasov theory'' can be traced back to Tanaka [36]. This paper can be seen as an attempt to advertize the ideas, power and simplicity of the pathwise appproach, not so easily extracted from [4, 9, 36]. As novel applications we discuss mean field convergence without a priori independence and exchangeability assumption; common noise and reflecting boundaries. Last not least, we generalize Dawson--Gärtner large deviations to a non-Brownian noise setting.

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